The USTR has now published a fact sheet providing a bit more detail on the new deal between the administraiton and congress (hat tip to Julian Ku at Opinio Juris). The idea is to make the 5 core principles subject to the same dispute settlement as commercial obligations, but (i) only insofar as they relate to trade and investment, and (ii) with no private rights of action.
It will be interesting to see if anything happens under these provisions. Experience may serve as a pathfinder for a multilateral arrangement relating trade to labor.